Linguistic Geometry And Its Applications

The notion of linguistic geometry is defined in this book. It is pertinent to keep in the record that linguistic geometry differs from classical geometry. Many basic or fundamental concepts and notions of classical geometry are not true or extendable in the case of linguistic geometry. Hence, for simple illustration, facts like two distinct points in classical geometry always define a line passing through them; this is generally not true in linguistic geometry. Suppose we have two linguistic points as tall and light we cannot connect them, or technically, there is no line between them. However, let's take, for instance, two linguistic points, tall and very short, associated with the linguistic variable height of a person. We have a directed line joining from the linguistic point very short to the linguistic point tall. In this case, it is important to note that the direction is essential when the linguistic variable is a person's height. The other way line, from tall to very short, has no meaning. So in linguistic geometry, in general, we may not have a linguistic line; granted, we have a line, but we may not have it in both directions; the line may be directed. The linguistic distance is very far. So, the linguistic line directed or otherwise exists if and only if they are comparable. Hence the very concept of extending the line infinitely does not exist. Likewise, we cannot say as in classical geometry; three noncollinear points determine the plane in linguistic geometry. Further, we do not have the notion of the linguistic area of well-defined figures like a triangle, quadrilateral or any polygon as in the case of classical geometry. The best part of linguistic geometry is that we can define the new notion of linguistic social information geometric networks analogous to social information networks. This will be a boon to non-mathematics researchers in socio-sciences in other fields where natural languages can replace mathematics.

Linguistic Geometry: From Search to Construction is the first book of its kind. Linguistic Geometry (LG) is an approach to the construction of mathematical models for large-scale multi-agent systems. A number of such systems, including air/space combat, robotic manufacturing, software re-engineering and Internet cyberwar, can be modeled as abstract board games. These are games with moves that can be represented by the movement of abstract pieces over locations on an abstract board. The purpose of LG is to provide strategies to guide the games' participants to their goals. Traditionally, discovering such strategies required searches in giant game trees. These searches are often beyond the capacity of modern and even conceivable future computers. LG dramatically reduces the size of the search trees, making the problems computationally tractable. LG provides a formalization and abstraction of search heuristics used by advanced experts including chess grandmasters. Essentially, these heuristics replace search with the construction of strategies. To formalize the heuristics, LG employs the theory of formal languages (i.e. formal linguistics), as well as certain geometric structures over an abstract board. The new formal strategies solve problems from different domains far beyond the areas envisioned by the experts. For a number of these domains, Linguistic Geometry yields optimal solutions.

Intelligent Systems can be defined as systems whose design, mainly based on computational techniques, is supported, in some parts, by operations and processing skills inspired by human reasoning and behaviour. Intelligent Systems must typically operate in a scenario in which non-linearities are the rule and not as a disturbing effect to be corrected. Finally, Intelligent Systems also have to incorporate advanced sensory technology in order to simplify man-machine interactions. Several algorithms are currently the ordinary tools of Intelligent Systems. This book contains a selection of contributions regarding Intelligent Systems by experts in diverse fields. Topics discussed in the book are: Applications of Intelligent Systems in Modelling and Prediction of Environmental Changes, Cellular Neural Networks for NonLinear Filtering, NNs for Signal Processing, Image Processing, Transportation Intelligent Systems, Intelligent Techniques in Power Electronics, Applications in Medicine and Surgery, Hardware Implementation and Learning of NNs.

In the areas of industry and engineering, AI techniques have become the norm in sectors including computer-aided design, intelligent manufacturing, and control. Papers in this volume represent work by both computer scientists and engineers separately and together. They directly and indirectly represent a real collaboration between computer science and engineering, covering a wide variety of fields related to intelligent systems technology ranging from neural networks, knowledge acquisition and representation, automated scheduling, machine learning, multimedia, genetic algorithms, fuzzy logic, robotics, automated reasoning, heuristic searching, automated problem solving, temporal, spatial and model-based reasoning, clustering, blackboard architectures, automated design, pattern recognition and image processing, automated planning, speech recognition, simulated annealing, and intelligent tutoring, as well as various computer applications of intelligent systems including financial analysis, artificial

Artificial intelligence (AI) is a branch of computer science that models the human ability of reasoning, usage of human language and organization of knowledge, solving problems and practically all other human intellectual abilities. Usually it is characterized by the application of heuristic methods because in the majority of cases there is no exact solution to this kind of problem. Soft computing can be viewed as a branch of AI that deals with the problems that explicitly contain incomplete or complex information, or are known to be impossible for direct computation, i.e., these are the same problems as in AI but viewed from the perspective of their computation. The Mexican International Conference on Artificial Intelligence (MICAI), a yearly international conference series organized by the Mexican Society for Artificial Intelligence (SMIA), is a major international AI forum and the main event in the academic life of the country’s growing AI community. In 2010, SMIA celebrated 10 years of activity related to the organization of MICAI as is represented in its slogan “Ten years on the road with AI”. MICAI conferences traditionally publish high-quality papers in all areas of artificial intelligence and its applications. The proceedings of the previous MICAI events were also published by Springer in its Lecture Notes in Artificial Intelligence (LNAI) series, vols. 1793, 2313, 2972, 3789, 4293, 4827, 5317, and 5845. Since its foundation in 2000, the conference has been growing in popularity and improving in quality.

Containing papers presented at the 2016 New Forest Conference on Complex Systems, this multi-disciplinary book presents new approaches for resolving complex issues that cannot be resolved using conventional mathematical or software models. Complex Systems occur in an infinite variety of problems encompassing fields as diverse as economics, the environment, humanities, social and political sciences, physical sciences and engineering. The papers in the book cover such topics as: Complex business processes; Supply chain complexity; Complex adaptive software; Management of complexity; Complexity in social systems; Complexity in engineering; Complex issues in biological and medical sciences; Complex energy systems Complexity and evolution.

In this book, for the first time, authors try to introduce the concept of linguistic variables as a continuum of linguistic terms/elements/words in par or similar to a real continuum. For instance, we have the linguistic variable, say the heights of people, then we place the heights in the linguistic continuum [shortest, tallest] unlike the real continuum (–∞, ∞) where both –∞ or +∞ is only a non-included symbols of the real continuum, but in case of the linguistic continuum we generally include the ends or to be more mathematical say it is a closed interval, where shortest denotes the shortest height of a person, maybe the born infant who is very short from usual and the tallest will denote the tallest one usually very tall; however this linguistic continuum [shortest, tallest] in the real continuum will be the closed interval say [1 foot, 8 feet] or [1, 8] the measurement in terms of feet. So, the real interval is a subinterval with which we have associated the real continuum in terms of qualifying unit feet and inches in this case.

Due to the rapid increase in readily available computing power, a corre sponding increase in the complexity of problems being tackled has occurred in the field of systems as a whole. A plethora of new methods which can be used on the problems has also arisen with a constant desire to deal with more and more difficult applications. Unfortunately by increasing the ac curacy in models employed along with the use of appropriate algorithms with related features, the resultant necessary computations can often be of very high dimension. This brings with it a whole new breed of problem which has come to be known as "The Curse of Dimensionality" . The expression "Curse of Dimensionality" can be in fact traced back to Richard Bellman in the 1960's. However, it is only in the last few years that it has taken on a widespread practical significance although the term di mensionality does not have a unique precise meaning and is being used in a slightly different way in the context of algorithmic and stochastic complex ity theory or in every day engineering. In principle the dimensionality of a problem depends on three factors: on the engineering system (subject), on the concrete task to be solved and on the available resources. A system is of high dimension if it contains a lot of elements/variables and/or the rela tionship/connection between the elements/variables is complicated.